Problem: Solve for $y$. $\dfrac94y-12=\dfrac14y-4$ $y=$
Solution: We need to manipulate the equation to get $ y $ by itself. $\begin{aligned} \dfrac94y-12&=\dfrac14y-4 \\\\ \dfrac94y-12 {-\dfrac14y} &= \dfrac14y-4{-\dfrac14y} &&\gray{\text{Subtract } \dfrac14y \text{ from each side.}}\\\\ 2y-12&=-4 &&\gray{\text{Combine like terms.}}\\\\ 2y-12{+12} &= -4{+12} &&\gray{\text{Add 12 to each side.}}\\\\ 2y &=8 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{2y}{{2}} &= \dfrac{8}{{2}} &&\gray{\text{Divide each side by 2.}}\\\\ y &= {4} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $y = { 4 }~~~~~~~~$ [Let's check our work!]